Lecture 11 Measurement Techniques A. Nassiri – ANL June 19, 2003

Microwave Physics and Techniques UCSB –June 2003 1 Introduction • Measurement rules, difficulty in voltage and current measurements, test equipment Noise Noise power, S/N, noise figure, equivalent noise temperature, noise figure of a cascaded circuit

Frequency measurements Frequency counter method, wavelength measurement method, wavemeter method

Detection devices Thermistor, barretter, thermocouple,

Power measurements Thermistor power meter, arrangements for low, medium and high power measurement

Microwave Physics and Techniques UCSB –June 2003 2 Attenuation measurements Insertion loss, substitution method

VSWR measurements

Introduction to S-parameters Reasons to use S-parameter, definition, signal flow graph, Properties

Microwave test equipment analyzers Purpose and operating principle of spectrum analyzer and network analyzer

Microwave Physics and Techniques UCSB –June 2003 3 Introduction

1. Rules of a “correct microwave” measurement

(a) know what parameters you want tested. (b) have a proper test arrangement. “Always check the power handling capacity of your microwave components and test equipment.” (c) know how to perform your test. (d) know how to interpret the results.

Plan ahead.

No calibrated, do not use for quantitative data.

2. Difficult or impossible in the measurement of voltage and current at microwave frequencies because

(a) voltage and current readings vary with position along the transmission line, (b) voltage and current are difficult to define in non-TEM transmission lines.

Microwave Physics and Techniques UCSB –June 2003 4 3. Test equipment

(a) sources: sweeper (YIG tuned oscillator), synthesizer, klystron oscillator, Gunn oscillator, ...

(b) receivers: power meter, spectrum analyzer, network analyzer, detector, frequency counter, wavemeter, noise figure meter, …

(c) auxiliary devices: attenuator, directional coupler, slotted line, coaxial cable, adapter, ,…

Microwave Physics and Techniques UCSB –June 2003 5 Noise Noise power (due to thermal noise) • • Noisy resistor v Noiseless R ,0o k n (t ) resistor v o R ,T k • n (t ) •

Planck’s black body radiation law, kT hf n kT rms voltage across a resistor R is e hf R kTν = 4 hf ()f df ∫ kT −1 e k hf << kT at hf −1 ≅ → νn = 4kTBR microwave frequencies T

Microwave Physics and Techniques UCSB –June 2003 6

• P• n Pn • • Noisy BPF Noiseless,

R T0 kRR 00 kRT0 k, B

lossless BPF ≡ •

• P • Load • Load n n R R 2  ν  νn =   = R = kTB  2  4

The maximum power delivered from the noisy resistor is Pn= kTB, which is considered equally across an entire microwave band.

A resistor temperature at 3000 k, noise power for a 10kHz bandwidth -17 receiver → Pn =4.14 × 10 W = -176dBW= -146dBm

At the standard temperature of 2900 k, the noise power available from a lossy passive network in a 1Hz bandwidth is -174dBm/Hz.

Microwave Physics and Techniques UCSB –June 2003 7 Signal-to-noiseS ratio (SNR) N d P s =10log Difficult to measure S NB Pn N d + P s + =10log P n Measurable quantity B Pn S N A receiverN produces a noise power of 200mW without signal, as signal is P applied, the output level becomesP 5W. P d + s + 5 =10log n =10log =14dB B n 0.2

Microwave Physics and Techniques UCSB –June 2003 8 Noise figure

A figure of merit to measure the degradation of SNR of a system

P = S + N i i i P0 = S0 + N0

R,T Noisy 0 network Si R G,B,T NFLoad NF S N NF ()i = S ≥1 dB =10log ≥ 0dB ()N o NF For a passive device withS G=1/LN and in thermal equilibrium at the temperature T, N = kTB = N , S =GS , 0 i o Si S N N ( ) = i = S0 Ni = L i ()o o

Microwave Physics and Techniques UCSB –June 2003 9 signal gain An noiseamplifier with input signal 100µW and the noise power is 1µW. The amplified gainsignal is 1W with noise power 30mW. 1000000 =10log = 40dB 100 30000 dB =10log = 44.7 > 40dB 1 NF NF S ()N 100 1 dB NF = S i = = 3 >1 S N dB = 4.7 > 0dB ()N o 1000 30 S N S N S An with NF 6dB has an input SNR=40dB, N NF i () = o → d = d − dB = 40 − 6 = 34dB ()o B i B

Microwave Physics and Techniques UCSB –June 2003 10 Equivalent noise temperature: the absolute temperature to generate the same noise power, not the physical temperature of the device equivalent noise temperature Te ≡ Pn /kB

Pn P • n White noise R source 0 NF S Load ≡ RRT e k N i • S N R ( ) =S o ()i Gk Pi=Si + Ni P0=S0 + N0 kT T B T ()+ = GS0 e B Noisy network R, T0 R 0 i Si G,B, Te Load T =1+ e ≥1 T T0 NF → e = ( −1)T0

Microwave Physics and Techniques UCSB –June 2003 11 Example:

0 A LNA (low noise amplifier) NF =2dB =1.585 →T0 = (NF-1)T=170 K

Microwave Physics and Techniques UCSB –June 2003 12 NF of a cascaded circuit

G , F G , F G , F NF S 1 1 1 1 ••• 1 1 N kT S S i N N B()N i 0 = i= ()i G S o k 0 N i N A three-stage amplifier i NF i G kT B T B Stage power gain noise figure  i i G  0 ∏ ()1 −1 0 ∏ 1 10 10dB 2 3dB 1  =1 kT =1 =  + B 2 20 13dB 4 6dB  0 0 k N ∏  NF 3 30 14.8dB 6 7.8dB =1  T B i i G  ()kT−1  2 B 0 ∏ =2  Total gain=6000=37.8dB + +L  k0 NF N  Total NF=2+[(4-1)/10]+[(6-  1)/(10×20)]=2.325=3.66dB ()−1T BG0 n  + kT 0B 

Microwave Physics and Techniques UCSB –June 2003 13 Frequency measurements

Two approaches: using frequency counter to measure frequency directly, and using probe to measure the wavelength in a transmission line.

Frequency counter approach

(1) Basic principle: direct counting <500MHz

Input Signal Conditioner Main Count Display Gate Time Gate Chain Base Generator

(2) Using frequency down-conversion techniques for microwave signals

ƒ Pre-scaling: divider circuit <2GHz

Microwave Physics and Techniques UCSB –June 2003 14 ƒTransfer oscillator down-conversion: use PLL to relate the harmonic relationship between the low frequency oscillator and the input microwave signal > 40GHz

Input signal PSD Power divider 9 PL CCT fs FIF1 To counter Comb generator f VCO fS = NfVCO-fIF1

Comb generator

fVCO ± fo FIF1 fs 9 9 FIF2 FIF1 ± Nfo To ratio counter

Microwave Physics and Techniques UCSB –June 2003 15 Harmonic heterodyne: use mixer to harmonically down convert the input microwave signal <20GHz

IF amp

Input signal Fs ± Kfi = fIF 9 To counter fs fIF

Kfi bus YIG pin counter switch control e filter

fi Comb generator multiplier Microprocessor

From counter time base fs = Kfi +fIF

Microwave Physics and Techniques UCSB –June 2003 16 Wavelength measurement approach

Gunn Oscillator PS SWR Meter

PS SWR

Fixed short Gunn Oscillator Variable Slotted Line Attenuator circuit c

c c 35dB • k

g a c 2 2 2π 2π k 2 2  2π  2π = ,λ = 2 ,β = = − k =   −   λ λ  λ   λc  f g c 2 2  1   1  Measure λ → =   +      λg   2a 

Microwave Physics and Techniques UCSB –June 2003 17 Distance between two adjacent minima is 1.9cm in a WR-90 .

f cm c cm a a cm 90 λ = 2×1.9 = 3.8 , = × 2.54 = 2.29cm g cm 100 2 2  1   1  =   +     cm  λg   2  2 cm 2  1   1  = 3×1010 / sec   +   =10.26 GHz  3.8   2× 2.29 

Microwave Physics and Techniques UCSB –June 2003 18 Wavemeter method

ƒ Wavemeter structure

Resistive material

Piston Cavity

Microwave Physics and Techniques UCSB –June 2003 19 Operating principle Cavity Input Output nλ d = g 2 Inputb Output

Transmission type Microwave Power Reaction type Meter Standing wave indicator Cavity frequency meter Variable precision attenuator Detector probe Microwave Source 1KHz Square Thermistor mount Wave Variable flap attenuator Slotted line Microwave Physics and Techniques UCSB –June 2003 20 Detection devices

Power detector: bolometer (thermistor and barretter), thermocouple voltage detector: crystal detector, Schottky barrier , GaAs barrier diode

Thermistor: a metallic-oxide component with a negative temperature coefficient of resistance

Barretter: a short length of platinum or wire with a positive temperature coefficient of resistance

Microwave Physics and Techniques UCSB –June 2003 21 Detection devices Thermocouple: a pair of dissimilar metal (Sb-Bi) wires joined at one end (sensing end) and terminated at the other end (reference end). The difference in temperature produces a proportional voltage.

Crystal detector: use the diode square-law to convert input microwave power to detector output voltage Diode Matching Low-pass Filter • Circuit • Microwave Low Input Frequency Output DC Return

DC return is as a ground for diode and an RF choke.

Microwave Physics and Techniques UCSB –June 2003 22 Detection devices

Schottky barrier or GaAs barrier diode: high sensitivity noise equivalent power (NEP): the required input power to produce, in 1Hz bandwidth, an output SNR = 1 tangential sensitivity (TSS): the lowest detectable microwave signal power NEP f TSS Vedio = ,∆ : Bandwidth 2.5 ∆f

Microwave Physics and Techniques UCSB –June 2003 23 Power Measurements Difficulty in measuring voltage or current at microwave frequencies → power measurement simpler and more precise

Power range: low power <0dBm, medium power 0dBm~40dBm, high power >40dBm

power detector sensitivity: diode ~-70dm, thermistor ~-20dBm

Thermistor power meter A • • R Wheatstone Bridge R Balance AC Ammeter Adust C • A • D v 10-kHz AC P0 R Source P1 RT Voltmeter • • Microwave B Power in

Microwave Physics and Techniques UCSB –June 2003 24 Power measurement arrangement ƒ Low power case

Consider desired frequency spectrum, circuit mismatch, sensor mismatch, sensor safe margin, accuracy, calibration

Generator Power RF Out Meter

LPF Attenuator Power DUT or BPF (optional) Sensor

Microwave Physics and Techniques UCSB –June 2003 25 Power measurement arrangement Medium power case: use directional coupler or attenuator at the DUT (device under test) output Thermistor Generator (0 dBm) Power Meter Power 1 Watt 10 dB Supply Circulator 50Ω Attenuator (+10 dBm) 1 Watt (+30 dBm) 2 1 Watt 3 dB 1 3 2 Watts 50Ω Attenuator Amplifier 20 dB under test Coupler Generator Power Thermistor Supply Circulator 50Ω (0 dBm) Power Meter 1 Watt (+30 dBm) 1 Watt 3 dB 30 dB 2 Watts 50Ω Attenuator Attenuator Amplifier under test

Microwave Physics and Techniques UCSB –June 2003 26 Power measurement arrangement High power case: use directional coupler in reverse direction Power Meter (0 dBm) Thermistor Mount

30 dB Maximum full Attenuator scale +10 dBm (2 Watts)

(+30 dB) 100 watts (+50 dBm) 1 2 20 dB Directional Power Coupler Amplifier 3

50 Ω, 1W Termination Microwave Physics and Techniques UCSB –June 2003 27 Attenuation Measurements P3 Insertion Loss P P1 2

Source Component Load

P4 P1: power to the load without DUT P2:IL powerdB to the load after inserting DUT P3: power dissipated inside DUT P4: power reflected fromP DUT P P dBm 1 =10log = 1()− P2 dBm () 2

Microwave Physics and Techniques UCSB –June 2003 28 IL

If Γ: DUT reflection coefficientT and T: DUT transmission coefficient, 2 2 2 1− Γ dB = −10log = −10logT 1− Γ 2 2 T = −10logP(1− Γ 2 )−10log P 2 P 1− Γ − P = −10log 1 4 −10log P 2 1 1 − P4 = loss due to reflection + loss due to transmission

P1 P1 –P4 P2

P4 Insertion loss is the characteristics of DUT itself. As input port and output ports are matched, IL= attenuation.

Microwave Physics and Techniques UCSB –June 2003 29 VSWR measurements

SWR Meter

SWR

Slotted Line Microwave Source Load (1 kHz AM) •

If E probe penetrates too far into the slotted line, → disturb the field distribution and detected signal too strong to drive the detector out of its square-law region.

Microwave Physics and Techniques UCSB –June 2003 30 S- Parameters

Problems to use Z- , Y- or H- parameters in microwave circuits ¾ Difficult in defining voltage and current for non-TEM lines ¾ No equipment available to measure voltage and current in complex value as ¾ Difficult to make open and short circuits over broadband ¾ Active devices not stable as terminated with open or short circuit. S-parameters of a two-port network

Z0 2-Port Z V V RL= Z0 0 1 Device 2 Z0 2V1

I e e e a1 1 e S21 b2

• • e S V1 11 V2 S22 b e I2 1 e • e • e e S12 a2 Z in Z out

Microwave Physics and Techniques UCSB –June 2003 31 Definitiona of S- Parameters V + b1 = 1 Z 0 : incident (power) wave at port 1 V V − a 1 = 1 Z 0 : reflected (power) wave at port 1 V V + V b2 = 2 Z 0 V : incident (power) wave at port 2 b V V − I V 2 = 2 S Z 0 : reflected (power)V wave at port 2 b S Z a I V S ij +i Z − + V − V = + + − , =S + + − , = 1 − 1 , = Z2 − 2 1 1 1 2 2 a2 S1 b j 2 0 a 0 0i Z 0      a k j V − 1 = 11 12 1 ,P = = j      i + V  2   21 22  2  V + k ie=V0, ≠ =0, ≠ j i I i k ai 1 * 1 2 1 2 Incident power to port i: = ℜ {}= − b 2 2 2 i

Microwave Physics and Techniques UCSB –June 2003 32 Properties of S- Parameters S b = 1 : reflection coefficient at port 1 with port 2 matched 11 a 1 a2 =0 S b = 2 : forward transmission coefficient with port 2 matched 21 a 1 a2 =0 S b 1 = : reversed transmission coefficient with port 1 matched 12 a 2 a1 =0 S b = 2 22 a : reflection coefficient at port 2 with port 1 matched 2 a1 =0

2 IL or power gain from port 1 to port 2 = −10log S 21 2 IL or power gain from port 2 to port 1 = −10log S12 2 2 RL at port 1 or port 2 = − 10 log S 11 or = −10log S 22

Microwave Physics and Techniques UCSB –June 2003 33 Properties of S- Parameters

a′ a1 S21 b2 b′ l 1 2 1 [S´] l2 • • • • S S• • • • 11 S22 Z0 [S] Z S j 0 S• • e • • b′1 • • • • a′2 b1 S12 a S e j S b 2 a ′ − 2βl1 ′ S − j 2β(l1 +l2 ) S 11 = 11 , 21 S= 21e b a 1 =a1 11 + 2S12 − 2β()l1 +l2 S − j 2βl2 S 12′ = 12 , 22′ = 22e a 2 = 1 21 + 2S 22

Reasons to use S-matrix in microwave circuit

(1) matched load available in broadband application (2) measurable quantity in terms of incident, reflected and transmitted waves

(3) termination with Z0 causes no oscillation (4) convenient to use in the microwave network analysis

Microwave Physics and Techniques UCSB –June 2003 34 Microwave analyzers Spectrum analyzer

Purpose: measure microwave signal spectrum, can also be used to measure frequency, rms voltage, power, distortion, noise power, , frequency modulation, spectral purity,...

Operating principle

Mixer IF Amp e Log/Lin Adjust 9 Amp Detector Bandwidth

Y X Horizontal Swept LO Sweep CRT Generator Amp Scan width Center frequency Scan time

Microwave Physics and Techniques UCSB –June 2003 35 Network analyzer

Purpose: measure two-port S-parameter of a microwave device or network, can also be used to measure VSWR, return loss, group delay, input impedance, antenna pattern, dielectric constant,….

Operating principle

Microwave Physics and Techniques UCSB –June 2003 36 Scalar network analyzer measures the magnitude of two-port S- parameters.

Hp8510 vector network analyzer

Microwave Physics and Techniques UCSB –June 2003 37